{"paper":{"title":"An improved maximal inequality for 2D fractional order Schr\\\"{o}dinger operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Jianwei Yang, Jiqiang Zheng","submitted_at":"2013-08-15T11:02:25Z","abstract_excerpt":"The local maximal inequality for the Schr\\\"{o}dinger operators of order $\\a>1$ is shown to be bounded from $H^s(\\R^2)$ to $L^2$ for any $s>\\frac38$. This improves the previous result of Sj\\\"{o}lin on the regularity of solutions to fractional order Schr\\\"{o}dinger equations. Our method is inspired by Bourgain's argument in case of $\\a=2$. The extension from $\\a=2$ to general $\\a>1$ confronts three essential obstacles: the lack of Lee's reduction lemma, the absence of the algebraic structure of the symbol and the inapplicable Galilean transformation in the deduction of the main theorem. We get a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3359","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}